Even Catholics don’t endorse prayer for those who died with no hope of salvation, like this guy who died while trying to commit another murder.
We know he was a hell-bent personality who did damnable things, but we do not know if he repented in the end.
As you know, St. Peter tells us in the Bible that a day is like 1,000 years to the Lord,and 1,000 years like a day. If that is so, then God could have stretched Tsarnaev's last nanosecond out into a month or so in God-time, when he could have repented of his sins.
We simply don't know. Haven't got a clue. Only God is the Master of Time and Space, and only Jesus Christ is the Judge of the living and the dead.
On the day that died Pope innocent III (who was evidently not very innocent) appeared to Saint Lutgarda in flames and told her that he was expiating three crimes that he had to make atonement for. He begged her and her fellow nuns for prayers, because otherwise, he said, he would have to stay in purgatory until the end of time.
I know some Episcopalians believe in the Biblical purgatory, and some don't. (I do know the Episcopalian Church observes All Souls Day, which is an official "Holy Day" to pray for the dead.) In any case, if Tsarnaev did manage, like the criminal crucified next to Jesus, to repent at the end, I imagine he might get a punishment just like Pope Guilty. Not damned, you understand, but still requiring -- considerable -- purification.
May the Lord, Who knows all things and can do all things according to His will, have mercy on Tsarnaev, on us, and on the whole world.